Numerical Solution of Anomalous Solute Transport in a Two-Zone Fractal Porous Medium

Khuzhayorov, Bakhtiyor; Usmonov, Azizbek; Kholliev, Fakhriddin

doi:10.1007/978-3-031-34127-4_10

Cited by 2 publications

(2 citation statements)

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“…In the zone with the mobile liquid, a convective-diffusion equation is used, taking into account the anomalous diffusion process. Further, we use the "mobile" The model of anomalous solute transport is written as [29][30][31]: µ are the degradation coefficients of the adsorbed substance in the mobile and immobile zones, respectively, x is the spatial coordinate, t is the time, and…”

Section: Introductionmentioning

confidence: 99%

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Anomalous Solute Transport Using Adsorption Effects and the Degradation of Solute

Khuzhayorov,

Viswanathan,

Kholliev

et al. 2023

Computation

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In this work, anomalous solute transport using adsorption effects and the decomposition of solute was studied. During the filtration of inhomogeneous liquids, a number of new phenomena arise, and this is very important for understanding the mechanisms of the filtration process. Recently, issues of mathematical modeling of substance transfer processes have been intensively discussed. Modeling approaches are based on the law of matter balance in a certain control volume using additional phenomenological relationships. The process of anomalous solute transport in a porous medium was modeled by differential equations with a fractional derivative. A new mobile—immobile model is proposed to describe anomalous solute transport with a scale-dependent dispersion in inhomogeneous porous media. The profiles of changes in the concentrations of suspended particles in the macropore and micropore were determined. The influence of the order of the derivative with respect to the coordinate and time, i.e., the fractal dimension of the medium, was estimated based on the characteristics of the solute transport in both zones. The hydrodynamic dispersion was set through various relations: constant, linear, and exponential. Based on the numerical results, the concentration fields were determined for different values of the initial data and different relations of hydrodynamic dispersion.

show abstract

Section: Introductionmentioning

confidence: 99%

“…. In contrast to [30], here we take other dimensions as The model of anomalous solute transport is written as [29][30][31]:…”

Section: Introductionmentioning

confidence: 99%

Anomalous Solute Transport Using Adsorption Effects and the Degradation of Solute

Khuzhayorov,

Viswanathan,

Kholliev

et al. 2023

Computation

View full text Add to dashboard Cite

show abstract

Model of solute transport in a porous medium with multi-term time fractional diffusion equation

Khuzhayorov,

Usmonov,

Kholliev

2024

International Scientific and Practical Conference on Actual Problems of Mathematical Modeling and Information Technology

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Numerical Solution of Anomalous Solute Transport in a Two-Zone Fractal Porous Medium

Cited by 2 publications

References 17 publications

Anomalous Solute Transport Using Adsorption Effects and the Degradation of Solute

Anomalous Solute Transport Using Adsorption Effects and the Degradation of Solute

Model of solute transport in a porous medium with multi-term time fractional diffusion equation

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